Problem: Simplify the following expression: $y = \dfrac{-15a + 45}{-40a + 40}$ You can assume $a \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-15a + 45 = - (3\cdot5 \cdot a) + (3\cdot3\cdot5)$ The denominator can be factored: $-40a + 40 = - (2\cdot2\cdot2\cdot5 \cdot a) + (2\cdot2\cdot2\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $y = \dfrac{(5)(-3a + 9)}{(5)(-8a + 8)}$ Dividing both the numerator and denominator by $5$ gives: $y = \dfrac{-3a + 9}{-8a + 8}$